5 papers · 1 filter
Declarative distributed algorithms as axiomatic theories in three-valued modal logic over semitopologies
Murdoch J. Gabbay
We illustrate how to formally specify distributed algorithms as declarative axiomatic theories in a modal logic, using as illustrative examples a simple voting protocol, a simple b…
Semiframes: the algebra of semitopologies and actionable coalitions
Murdoch J. Gabbay
We introduce semiframes (an algebraic structure) and investigate their duality with semitopologies (a topological one). Both semitopologies and semiframes are relatively recent dev…
Semitopology: distributed collaborative action via topology, algebra, and logic
Murdoch J. Gabbay
We introduce semitopologies, a generalisation of point-set topology that removes the restriction that intersections of open sets need necessarily be open. The intuition is that poi…
A declarative approach to specifying distributed algorithms using three-valued modal logic
Murdoch J. Gabbay, Luca Zanolini
We present Coalition Logic, a three-valued modal fixed-point logic designed for declaratively specifying and reasoning about distributed algorithms, such as the Paxos consensus alg…
Semitopology: a topological approach to decentralised collaborative action
Murdoch Gabbay
We introduce semitopology, a generalisation of point-set topology that removes the restriction that intersections of open sets need necessarily be open. The intuition is that point…